What is the smallest positive number that is evenly divisible by all of the numbers from 1 to 20?

Ruby

(400..2432902008176640000).step(20).each do |i|
   val = (1..20).to_a.select{|x| i%x==0}&(1..20).to_a
   if val.count == 20
     puts i
     exit
   end
end

Use the product of the LCM's

require 'rational'
(1..20).inject(1) { |result, n| result.lcm n }


ruby-1.9.2-p180 :004 > (1..3).inject(1) { |result, n| result.lcm n }
 => 6 
ruby-1.9.2-p180 :005 > (1..4).inject(1) { |result, n| result.lcm n }
 => 12 
ruby-1.9.2-p180 :006 > (1..5).inject(1) { |result, n| result.lcm n }
 => 60 
ruby-1.9.2-p180 :007 > (1..6).inject(1) { |result, n| result.lcm n }
 => 60 
ruby-1.9.2-p180 :008 > (1..7).inject(1) { |result, n| result.lcm n }
 => 420 
ruby-1.9.2-p180 :009 > (1..8).inject(1) { |result, n| result.lcm n }
 => 840 
ruby-1.9.2-p180 :010 > (1..9).inject(1) { |result, n| result.lcm n }
 => 2520 
ruby-1.9.2-p180 :011 > (1..10).inject(1) { |result, n| result.lcm n }
 => 2520 
ruby-1.9.2-p180 :012 > (1..11).inject(1) { |result, n| result.lcm n }
 => 27720 
ruby-1.9.2-p180 :013 > (1..12).inject(1) { |result, n| result.lcm n }
 => 27720 
ruby-1.9.2-p180 :014 > (1..13).inject(1) { |result, n| result.lcm n }
 => 360360 
ruby-1.9.2-p180 :015 > (1..14).inject(1) { |result, n| result.lcm n }
 => 360360 
ruby-1.9.2-p180 :016 > (1..15).inject(1) { |result, n| result.lcm n }
 => 360360 
ruby-1.9.2-p180 :017 > (1..16).inject(1) { |result, n| result.lcm n }
 => 720720 
ruby-1.9.2-p180 :018 > (1..17).inject(1) { |result, n| result.lcm n }
 => 12252240 
ruby-1.9.2-p180 :019 > (1..18).inject(1) { |result, n| result.lcm n }
 => 12252240 
ruby-1.9.2-p180 :020 > (1..19).inject(1) { |result, n| result.lcm n }
 => 232792560 
ruby-1.9.2-p180 :021 > (1..20).inject(1) { |result, n| result.lcm n }
 => 232792560